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Journal of Applied Mathematics
Volume 2014, Article ID 798670, 6 pages
http://dx.doi.org/10.1155/2014/798670
Research Article

The Lattice of Intuitionistic Fuzzy Filters in Residuated Lattices

School of Science, Linyi University, Linyi, Shandong 276005, China

Received 6 November 2013; Accepted 10 April 2014; Published 29 April 2014

Academic Editor: Ch. Tsitouras

Copyright © 2014 Zhen Ming Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Ward and R. P. Dilworth, “Residuated lattices,” Transactions of the American Mathematical Society, vol. 45, no. 3, pp. 335–354, 1939. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. F. Esteva and L. Godo, “Monoidal t-norm based logic: towards a logic for left-continuous t-norms,” Fuzzy Sets and Systems, vol. 124, no. 3, pp. 271–288, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. P. Hájek, Metamathematics of Fuzzy Logic, Kluwer Academic, Dordrecht, The Netherlands, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  4. C. C. Chang, “Algebraic analysis of many valued logics,” Transactions of the American Mathematical Society, vol. 88, pp. 467–490, 1958. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. J. Wang, An Introduction to Mathematical Logic and Resolution Principle, Science in China Press, Beijing, China, 2003.
  6. E. Turunen, Mathematics Behind Fuzzy Logic, Physica, Heidelberg, Germany, 1999. View at MathSciNet
  7. B. van Gasse, G. Deschrijver, C. Cornelis, and E. E. Kerre, “Filters of residuated lattices and triangle algebras,” Information Sciences, vol. 180, no. 16, pp. 3006–3020, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. E. Turunen, “Boolean deductive systems of BL-algebras,” Archive for Mathematical Logic, vol. 40, no. 6, pp. 467–473, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. M. Kondo, “Filters on commutative residuated lattices,” in Integrated Uncertainty Management and Applications, vol. 68, pp. 343–347, Springer, Berlin, Germany, 2010. View at Publisher · View at Google Scholar
  10. L. Liu and K. Li, “Boolean filters and positive implicative filters of residuated lattices,” Information Sciences, vol. 177, no. 24, pp. 5725–5738, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. Y. Zhu and Y. Xu, “On filter theory of residuated lattices,” Information Sciences, vol. 180, no. 19, pp. 3614–3632, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. M. Haveshki, A. B. Saeid, and E. Eslami, “Some types of filters in BL algebras,” Soft Computing, vol. 10, no. 8, pp. 657–664, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. M. Kondo and W. A. Dudek, “Filter theory of BL algebras,” Soft Computing, vol. 12, no. 5, pp. 419–423, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. A. B. Saeid and S. Motamed, “Normal filters in BL-algebras,” World Applied Sciences Journal, vol. 7, pp. 70–76, 2009. View at Google Scholar
  15. E. Turunen, “BL-algebras of basic fuzzy logic,” Mathware & Soft Computing, vol. 6, no. 1, pp. 49–61, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. Rosenfeld, “Fuzzy groups,” Journal of Mathematical Analysis and Applications, vol. 35, no. 3, pp. 512–517, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. J. N. Mordeson and D. S. Malik, Fuzzy Commutative Algebra, World Scientific, London, UK, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  19. T. Head, “A metatheorem for deriving fuzzy theorems from crisp versions,” Fuzzy Sets and Systems, vol. 73, no. 3, pp. 349–358, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. T. Head, “Erratum to “A metatheorem for deriving fuzzy theorems from crisp versions',” Fuzzy Sets and Systems, vol. 79, no. 2, pp. 277–278, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  21. I. Jahan, “The lattice of L-ideals of a ring is modular,” Fuzzy Sets and Systems, vol. 199, pp. 121–129, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. Y. B. Jun, Y. Xu, and X. H. Zhang, “Fuzzy filters of MTL-algebras,” Information Sciences, vol. 175, no. 1-2, pp. 120–138, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  23. L. Liu and K. Li, “Fuzzy filters of BL-algebras,” Information Sciences, vol. 173, no. 1–3, pp. 141–154, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. J. L. Zhang and H. J. Zhou, “Fuzzy filters on the residuated lattices,” New Mathematics and Natural Compution, vol. 2, no. 1, pp. 11–28, 2006. View at Publisher · View at Google Scholar
  25. K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. Z. Xue, Y. Xiao, W. Liu, H. Cheng, and Y. Li, “Intuitionistic fuzzy filter theory of BL-algebras,” International Journal of Machine Learning and Cybernetics, vol. 4, no. 6, pp. 659–669, 2013. View at Publisher · View at Google Scholar